Year: 2026
Type: preprint
Abstract: In this paper, we study natural determinantal point processes on Stein manifolds defined by canonical sections and plurisubharmonic weight functions. We present a natural condition on the weights under which these processes satisfy a large deviation principle with a good rate function given by the Fenchel--Legendre transform of the pluripotential equilibrium energy. Along the way, we prove some pluripotential theoretic results on Stein manifolds, such as the $C^{1,1}$ regularity of appropriate envelopes. These results are noncompact analogues of results of Berman and Berman--Boucksom on compact Kähler manifolds.
Source: arXiv (Cornell University)
Author: Eum, Kiyoon
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2224106632, G7764104633
OpenAlex ID: W7221767901